Electronic structure of BaLi. II. First observation of the Ba6,7Li spectrum: Analysis of the (2)2Π→X 2Σ+ system
J. D’Incan, C. Effantin, A. Bernard, G. Fabre, R. Stringat, A. Boulezhar, and J. Vergès
Citation: The Journal of Chemical Physics 100, 945 (1994); doi: 10.1063/1.466576 View online: http://dx.doi.org/10.1063/1.466576
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Electronic structure of Bali. II. First observation of the Ba
6,7U spectrum:
Analysis of the (2)2n .... X 2~ + system
J. D'fncan and C. Effantin
Laboratoire de Spectrometrie Ionique et Mo!eculaire. C.N.R.S. et Universite Claude Bernard. Lyon 1, 43 Boulevard du 11 Novembre 1918. 69622 Villeurbanne. France
A. Bernard
Observatoire de Lyon. C.N.R.S. et Universite Claude Bernard. Lyon 1, 69561 Saint-Genis-Laval. France G. Fabre and R. Stringat
Laboratoire d'Optique Atomique et Mo!eculaire. Faculte des Sciences U.N.S.A .• 06108 Nice. France A. Boufezhar
Laboratoire de Physique Atomique et Mo!eculaire. Universite Hassan II, Faculte des Sciences. Ain Chok.
B.P. 5366. Mliarif, Casablanca. Morocco
J. Verges
Laboratoire Aime Cotton. CNRS II, 914050rsay, France (Received 1 June 1993; accepted 5 October 1993)
The thermal emission at high temperature (1100 'C) of BaLi has been analyzed spectroscopically at high resolution with a Fourier transform spectrometer. Molecular emission in the infrared region is observed and is ascribed to a transition from the (2)2n state towards the ground state X 2l:+ of BaLi. These states (among several others) have been predicted from ab initio calculations [see part I, A. R. Allouche and M. Aubert-Frecon, J. Chern. Phys. 100, 938 (1994)]. Very good agreement is observed between theoretical predictions and experiment for the energy of the (2)2n state and spectroscopic constants of both states. Both isotopic species Ba7Li and Ba6Li have been investigated and molecular parameters are derived from the analysis of the (2)2n-.x 2l:+(O,0) band (the one analyzable band). No irregularities appear in the rotational structure.
Principal constants (in cm- I) for X 2l:+(v=0) and (2)2n(v=0) states of Ba7Li are as follows:
State (2)2n(v=0) X2l:+(v=0)
T 7823.0
O.
A 530.3
B 0.204 16 0.19163
0.633 0.746 The spin-splitting
r
parameter in the lower state, A-doublingp and q parameters in the upper state, and their rotational dependence are also evaluated. Isotopic relations between corresponding rotational constants of Ba 7Li and Ba6Li are verified to a good approximation.I. INTRODUCTION
Recent results obtained in our group have been re- ported concerning the study of the low-lying electronic states of barium compounds BaH, BaD, and BaF,I-3 par- ticularly the states issuing from the lowest excited config- uration 6s5d of neutral Ba 2l: +, 2n, and 2 A. These states were well interpreted in terms of a complex since the en- ergies of the observed transitions implying them could be reproduced, in spite of the strong interactions, with an accuracy close to the high experimental precision. A the- oretical study of the electronic structure of BaH (Ref. 4) resulted in a realistic positioning in energy of these states.
Later on, the electronic spectrum of the analogous mole- cule CaF was investigated, 5.6 and the (1) 2 A state could be characterized for the first time at an energy in agreement
with theoretical predictions 7 based on ligand field calcula- tions with model potential functions. Similar agreement has been found for the lowest states of BaCI whose (1) 2 A state was recently characterized. 8
Encouraged by the predictive ability of the theory for this type of molecule, we have searched for the spectrum of BaLi whose relatively simple electronic structure appears suitable for ab initio calculations (see part I, Ref. 9). These establish the ground state as 2l: + and the first excited states (1)2n, (2)2l:+, and (2)2n, respectively, about 3500, 6100, and 7900 cm - I above.
Given the low energy of these first electronic states, it seemed useful to study the infrared thermal emission of a high temperature source. It turned out that the spectrum of the (2) 2 n -. X 2l: + system could be recorded between 7000 and 9000 cm - I. The aim of the present paper is to report the rotational analysis of the (0,0) band for both isotopic species Ba7Li and Ba6Li.
II. EXPERIMENT
The BaLi molecular spectrum was observed in the thermal emission of a heat pipe containing a mixture of barium and lithium in the presence of argon as a buffer gas at a pressure of 20 Torr (at room temperature) and heated at a temperature of 1100 'C. Under these conditions, the partial pressures of Ba and Li were about the same, 20 and 30 Torr, respectively. Ba7Li and Ba6Li spectra were inves- tigated in two series of experiments. The molecular emis- J. Chern. Phys. 100 (2), 15 January 1994 0021-9606/94/100(2)/945/5/$6.00 @ 1994 American Institute of Physics 945 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
946 D'incan et al.: Electronic structure of Bali. II. Spectrum
sion was analyzed in the infrared region, between 4000 and 8000 em-I, with the Fourier transform spectrometer of the Laboratoire Aime Cotton at Orsay, France. The resolution of the spectrometer system corresponded to a linewidth between 34 X 10-3 and 13 X 10-3 cm -I, the recording times ranging from 1 to 5 h. The precision achieved in the relative line wave number measurements was about 0.002 cm - I in the most favorable conditions.
III. OBSERVATIONS AND ANALYSIS
Two spectral regions of well-marked rotational struc- ture degraded towards shorter wavelengths appear, begin- ning at about 7550 and 8080 cm -I. The first one shows three pronounced heads, the least intense at 7553.21 cm-I, and two stronger heads of about equal intensities at 7556.11 and 7556.66 cm -I for Ba7Li. In all, six branches can be recognized-four strong branches, a branch of av- erage intensity corresponding to the head at 7553.21 cm-I, and a faint one running throughout. The same structure is observed for the Ba6Li isotopomer with a small shift to- wards shorter wavelengths of the corresponding heads [Fig. 1 ( a) ]. The second spectral region of interest shows three strong branches, two of which form heads (at 8081.62 and 8087.22 cm- I for Ba7Li). In addition, three faint branches can be detected for Ba6Li (only one for Ba7Li). Again, a small isotope shift effect, of the same order of magnitude, appears between spectra of the two species [Fig. 1 (b)].
First attempts at a rotational analysis were made on Ba6Li rather than the Ba7Li spectrum since spectrograms of higher signal-to-noise ratio were obtained for this spe- cies.
Two series of equal differences (within experimental accuracy) were readily found in the band at 7550 cm- I between line wave numbers in the four strongest branches, those lines corresponding to head-forming branches on one hand, and the two remaining ones on the other hand. The hypothesis of a 2II_2}: transition was considered and ap- peared to be the solution, allowing us to account for the whole set of observational data. Indeed, an arrangement of these four branches as PI and PQ12 for the head-forming branches, and QI and QRI2 for the other two, yielded series of equal differences PI (N)-PQI2 (N) = QI (N)-QR 12 (N) (N being a running number), which could also be found be- tween branches in the band at 8080 cm -I. These were then interpreted as Qp21 (N)-Q2(N)
=
RQ21 (N)-R 2(N) of the2II3/2-2}: component, the differences representing the spin splitting in the lower state, The absolute numbering was then derived and this led to the interpretation of the lines in the remaining branches.
A part of the Ba6Li spectrum showing few successive rotational lines in the six branches of the 2II1I2-2}: subband is reproduced in Fig. 2. The system appears limited to this unique rotationally analyzable band that is shown to be the (0,0) band from the observed isotope effect. The rotational structure can be followed up to high values of N (about 115) in the strongest branches. The principal heads in the (1,1), 2II1I2-2}: subband only, though not well marked,
can be positioned at about 7583.7 cm- I for Ba7Li and 7587.3 cm- I for Ba6Li.
IV. RESULTS AND DISCUSSION
Line wave numbers for each isotopomer were entered in a global adjustment and reduced to a set of molecular constants. The program used compares the experimental data to the corresponding model predictions calculated from approximate starting values of the parameters. These are then optimized iteratively using a nonlinear least- squares procedure, until the convergence criterion is ful- filled. The energies of the levels are calculated in appropri- ate subroutines from term-value formulas
CZ}:
states) or by diagonalizing energy matrices CZ II states).The rotational energies of the spin components F I and F2 in the X 2}:+ state, which is well described by Hund's case (b) coupling scheme, are expressed, for a given vibra- tional level, by the formulas
FI (N) =Fe(N)
=BN(N+ 1) -D[N(N+ 1) ]2+H[N(N+ 1)]3 +y'N/2,
F 2(N) =F feN)
=BN(N+ 1) -D[N(N+1) ]2+H[N(N+ 1)]3 -y'(N+ 1)/2,
where FI and F2 refer to J=N
+
1/2 and J=N -1/2, re- spectively. Band D are the rotational constants and y' is the effective spin splitting parameter. A polynomial expan- sion in N(N+
1) is used to represent centrifugal distortion corrections to the true spin splitting y parameter of the formy'=y+yNN(N+ 1) +YNN[N(N+ 1) ]2,
The energies of the rotational levels in the upper state
(2)2II, which is best represented by Hund's case (a) owing to the large value of its spin-orbit coupling constant, are the eigenvalues, for each J and e/
f
parity component of a given vibrational level, of two 2 X 2 matrices which repre- sent the effective Hamiltonian. Matrix elements have been taken as follows:0/211/2) =T-A/2+ (B-A J) (X
+
1) -D[ (X+
1)2 +X] +H[ (X+
1)3+X(3X+
1)]-AJJ[3(X
+
1)2+X]l2+p'[ 1 =F (X+
1) 1I2]12+q' [X +2=F2(X+
1) 112]12,(3/213/2) =T+A/2+ (B+AJ)(X -1) -D[ (X _1)2 +X] +H[ (X -1)3+X(3X -1)]
+AJJ[3(X -1)2+X]l2+q'X/2,
<
11213/2) = _XI/2{B-2DX +H(3X2+X+
1) -AJJ-q'[ -1 ± (X
+
1)1I2]12+p'/4},J. Chern. Phys., Vol. 100, No.2, 15 January 1994
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D'incan et af.: Electronic structure of Bali. II. Spectrum 947
(0-0)
(b)
(0-0)
(0-0)
where X = (J -1/2) (J
+
3/2) and the upper and the lower signs refer to e and/components, respectively. The param- eters involved have the usual definitions (see, e.g., Ref.10). However, the molecular parameters being correlated, all the terms cannot be determined independently. A choice has been made in associating the A-doubling param- eters p+, q+ (corresponding to 2n_2l:+ interactions) and p_, q_ (corresponding to 2n_2l:- interactions), which assumes that 2l:+ interactions with (2)2n are preponder- ant. So, the effective A-doubling parameters p=p+ -p_
(I-I)
and q = q + - q _ are determined, the other parameters T, A, and B being very slightly affected (see Ref. 11 for more details). Centrifugal distortion effects are approximated by adding polynomial expansions in J( J
+
1) to p and q of the formJ. Chem. Phys., Vol. 100, No.2, 15 January 1994
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948 D'incan et al.: Electronic structure of Bali. II. Spectrum
Ba6U: (2)2nI/2 ~ )(-117 (0-0)
42.5 44.5 46.5 48.5
PI
38.5 40.5 42.5 44.5 46.5
PQI2
18.5 20.5 22.5 24.5 26.5
QI
18.5 20.5 22.5 24.5 OR,
I 12
'v"",
1~ IA. \ ll~ \ v ~ ~ , \ ~ "'I \0 " \)
1.wl ~(V~V~W-~.\ v...
R,13.51
1
15.5
1
17.5 II
19.5 L °P1253.5 55.5 57.5
7yO 7y2 7y4 I I 1 I
75r
~ ~ ~ em·1FIG. 2. Part of the ~a6Li spectrum showing a few rotational lines in the six branches of the (2)2111/2_X 21;+ (0,0) subband.
Nevertheless, this classical 13-parameter model for 211 states allows the observation~ to be represented ade- quately only for lines of J smaller than about 60.5. The standard deviation between observed and calculated line wave numbers is then 0.0023 cm - I in this range, i.e., it approaches the experimental accuracy for both iso- topomers. The model appears less and less satisfactory as the Jmax of the fit is increased. So the standard deviations increase up
to 0.0060 cm-I with Jmax reaching 80.5, with individual deviations between observed and calculated line wave num- bers that increase very rapidly as J approaches Jmax . For Jmax greater than 90.5, the model becomes less and less satisfactory with standard deviations of the fits amounting to 0.030 and 0.078 cm-I, respectively, for Ba7Li and Ba6Li when all the line wave numbers are introduced. Different tests on parameters have been done in order to improve the
TABLE I. Effective molecular constants (em-I) for the X 21;+ and (2)211 states of Ba6.7Li.'
Ba7Li Ba6Li
Isotopically X21;+ (v=O) Experimental Theoretical Experimental scaled values
T 0 0 0
B 0.1916279(97) 0.194 0.221 812(10) 0.2220
106 D 0.7460(10) 0.989 O( 16) LOO
IOIIH -0.107(13) -0.2570(77)
r 0.046 181 (30) 0.053495(39) 0.05349
105 rN -0.13495(91) -0.1810(12) -0.181 1
1010 rNN 0.1179(62) 0.1766(86) 0.1832
(2)211 (v=O)
T 7823.014(1 ) 7935 7 824.090(1) 7824.06
A 530.316(1) 485 530.486(1 ) 530.32
103 AI 0.27972(42) 0.33061 (43) 0.324
107 A JJ 0.1138(44) 0.156 13(43)
1016 A JJJJ 0.2878(20) 0.5327(17)
B 0.204 158( 11) 0.207 0.236386(12) 0.2365
106 D 0.6628(24) 0.8855(20) 0.889
1012 H -0.48(17) -0.893(99)
P 0.171 139(42) 0.197826(50) 0.1982
105 PI -0.123 4( 17) -0.1619(17) -0.166
109 PJJ -0.069 2( 16) -0.1153(13)
103 q 0.174(12) 0.177( 13) 0.233
107 ql -0.254(32) -0.1566(28)
1011 qll 0.168(22) 0.091(15)
'Numbers in parentheses represent 2a in units of the last digit.
J. Chern. Phys., Vol. 100, No.2, 15 January 1994
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D'incan et sl.: Electronic structure of Bali. II. Spectrum 949
model. It has been shown that the only way to account for all the observations is to introduce an additional term in the description of the spin-orbit interaction corresponding to a parameter AJJJJ whose angular dependence must be taken as [J(J+
l)f
times the angular dependence for AJJ • In these conditions, the effect is almost entirely reduced.Corresponding results are reported in Table I. This set of molecular constants permits the observed spectra to be ap- proached to standard deviations of 0.0030 em -I for Ba 7Li (900 line wave numbers) and 0.0043 cm- I for Ba6Li (1200 line wave numbers).12 These values, significantly higher than the experimental accuracy, reveal the difficulty for the model to fit the energies of the very last rotational levels in the (2)2II state. Certainly, the present model is too simple to properly represent the large effective spin- orbit interaction in (2)2II complicated by interactions with the numerous surrounding states.
An estimate of the first vibrational intervals can be obtained from the formula D=4.nJ/CJl. Using values in Table I, one finds a>"=197.5 em-I, a>'=227.8 cm- I for Ba7Li and a>"=207.6 cm- I, a>'=236.4 cm- I for Ba6Li, i.e., a difference a>' -a>" close to 30 cm -I for both isotopic species given the uncertainty of this determination. There- fore, the bandheads observed at 7583.7 and 7587.3 cm- I, respectively, for Ba7Li and Ba6Li, about 27.6 and 30.5 em -I away from the principal heads of the analyzed
2rrI/2-2l:(V',v") transition, do belong to the (v'
+
1, v"+
1) subbands. From the observed isotope shifts be- tween corresponding bands avv',v"= -1.08 cm-I (be- tween origins) and aVv'+I,v"+I=-3.6 cm-I (between heads), it appears unambiguously that these are in fact (0,0) and (1,1). Indeed, the simplified isotopic relation dVv',v" = (1 - p)[w;(v'+
112) - w;(v"+
112)], which is a good approximation since p is only slightly different from 1 (p= 1.076262), gives avoo= -1.05 cm- I- I '
andAvI,I=-3.15cm .
Isotopically scaled values of the principal spectro- scopic constants of Ba6Li calculated from the observed val- ues for Ba7Li are given in Table I for comparison with the determined constants.
Theoretical results presented in part I were revealed very helpful in identifying and analyzing the experimental
spectra. Among the many electronic states of BaLi antici- pated on the basis of elaborate models, two have been stud- ied in detail in the present work-the ground state X 21: + and the (2)2II state. Theoretical values for the rotational constants of both states and the spin-orbit constant and energy of (2)2II appear close to the observed values (see Table I for comparison). Also, the first vibrational inter- vals estimated above are of comparable magnitUde with the theoretical values
w:
= 200.8 andw;
= 235.0 em -I found when spin-orbit interactions are neglected. Hence, the re- alistic predictive possibilities shown by the models should enable further experimental investigations of the electronic spectrum of this molecule, even by using laser induced fluorescence techniques.ACKNOWLEDGMENT
The authors thank Dr. R. F. Barrow from Oxford Uni- versity (England) for critical reading of the manuscript.
I A. Bernard, C. Effantin, J. d'Incan, G. Fabre, R. Stringat, and R. F.
Barrow, Mol. Phys. 67, 1 (1989).
2C. Effantin, A. Bernard, J. d'Incan, G. Wannous, J. Verges, and R. F.
Barrow, Mol. Phys. 70, 735 (1990).
3 A. Bernard, C. Effantin, J. d'lncan, J. Verges, and R. F. Barrow, Mol.
Phys. 70, 747 (1990).
4 A. R. Allouche, G. Nicolas, J. C. Barthe1at, and F. Spiegelmann, J.
Chern. Phys. 96, 7646 (1992).
5J. d'Incan, C. Effantin, A. Bernard, J. Verges, and R. F. Barrow, J.
Phys. B 24, L71 (1991).
6J. Verges, C. Effantin, A. Bernard, A. Topouzkhanian, A. R. Allouche, J. d'Incan, and R. F. Barrow, J. Phys. B 26, 279 (1992).
7 A. R. Allouche, G. Wannous, and M. Aubert-Frecon, Chern. Phys. 170, 11 (1993).
8c.
Amiot and J. Verges, Chern. Phys. Lett. 185,310 (1991).9 A. R. Allouche and M. Aubert-Frecon, J. Chern. Phys. 100, 938 (1994).
lOR. N. Zare, A. L. Schme1tekopf, W. J. Harrop, and D. L. Albritton, J.
Mol. Spectrosc. 46, 37 (1973).
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413,829 (1993).
12See AlP document no. PAPS JCPSA-1OO-945-14 for 14 pages of a catalogue of line wave numbers. Order by PAPS number and journal reference from American Institute of Physics, Physics Auxiliary Publi- cation Service, 500 Sunnyside Boulevard, Woodbury, New York 11797- 2999. The price is $1.50 for each microfiche (60 pages) or $5.00 for photocopies of up to 30 pages, and $0.15 for each additional page over 30 pages. Air mail additional. Make checks payable to the American Institute of Physics.
J. Chern. Phys., Vol. 100, No.2, 15 January 1994
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